Question

In developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. How large a sample should be taken if the desired margin of error is two minutes at a 95% level of confidence? How large a sample should be taken for a 99% level of confidence? Use a planning value for the population standard deviation of 7 minutes.

95% Confidence (to the nearest whole number) :

99% Confidence (to the nearest whole numer):

Answer 1

Solution :

Given that,

Population standard deviation = = 7

Margin of error = E = 2

a) At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2  = 0.025

Z_/2 = 1.96

sample size = n = [Z_/2* / E] ²

n = [ 1.96 * 7 / 2 ]²

n = 47.05

Sample size = n = 48

b) At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2  = 0.005

Z_/2 = 2.576

sample size = n = [Z_/2* / E] ²

n = [ 2.576 * 7 / 2 ]²

n = 81.28

Sample size = n = 82